PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
80015^90431-9663209Lelio R Paula04/2013
8002(172*10^63202-1)/963204Serge Batalov12/2014
8003(43*10^63200+83)/963201Robert Price08/2017
80042^209914-1600563191Enzo Doria04/2013
80053*6^81190-563179Lelio R Paula09/2014
80062^209820+425763163Lelio R Paula10/2011
800799^31648+263158Lelio R Paula05/2013
800816976^5253+5253^1697663158Hans Havermann01/2017
80092^209790+6763154Lelio R Paula08/2011
8010145878#-p(145878)63152Henri Lifchitz12/2018
80112^209759+9019563144Lelio R Paula02/2013
8012145823#+21150763142Arkadiusz Wesolowski03/2013
80132^209707+51363129Lelio R Paula10/2011
8014(3^132314-8)/1763129Lelio R Paula04/2012
8015(2*10^63117+7)/963117Erik Branger03/2011
80169*2^209654-763114Lelio R Paula04/2014
801784304!6-963112Robert Price08/2018
801811^60598-1463107Lelio R Paula05/2013
801915103^15078+15078^1510363106Hans Havermann01/2017
802015346^12941+12941^1534663103Hans Havermann01/2017
80213^132253+7663101Lelio R Paula04/2013
8022(56*10^63100+403)/963101Robert Price10/2017
802317549^3936+3936^1754963090Hans Havermann01/2017
8024(55459*2^209553+1)/42363084Lelio R Paula06/2014
8025(331^25033-1)/33063077Eric Chen09/2017
802720^48480+3163074Lelio R Paula06/2013
8026(26*10^63073-23)/363074Robert Price08/2016
80282^209499+7625363066Enzo Doria04/2016
802911^60546-1134063053Enzo Doria12/2012
80302^209426+5788963044Yves Minet02/2010
8031(22699*2^209405+1)/2163041Lelio R Paula06/2014
80325^90189+5463040Lelio R Paula04/2013
8033(22*10^63034-73)/363035Robert Price09/2017
8034(314021^11467+1)/31402263029Faysal YAtim05/2008
8035V(301486)63007Henri Lifchitz05/2003
8036(31*2^209298+1)/9563005Lelio R Paula08/2012
8037(27*2^209245+1)/562990Lelio R Paula08/2012
80386^80946-5^(80946-1)62989Robert Price05/2016
8039467^23596+23596^46762986Norbert Schneider08/2016
8040(7*2^209212-1)/362980Lelio R Paula01/2014
8041(27*2^209206-1)/1162978Lelio R Paula01/2014
80421456^19909+19909^145662976Serge Batalov05/2014
8044(3^131964-5)/18521239662955Lelio R Paula04/2012
804335^40772-146662955Enzo Doria03/2013
80455^90064-1370662953Enzo Doria02/2013
8046(22*10^62926+257)/962927Robert Price11/2017
8047(13*10^62914+401)/962915Robert Price10/2017
80482^208993+10762914Lelio R Paula08/2011
80492^208993+7762914Lelio R Paula08/2011
8050189^27636-262913Lelio R Paula10/2017
8051(2^208948-7)/26162898Lelio R Paula03/2012
8052(151*10^62879-1)/362881Robert Price04/2017
805315^53464-8262879Lelio R Paula05/2013
80542^208843-11292162869Enzo Doria06/2014
80552^208779+8162849Henri Lifchitz01/2007
8056159^28548+15862846Norbert Schneider12/2018
8057(21181*2^208780+1)/899383884162844Lelio R Paula06/2014
8058(73*10^62824+17)/962825Robert Price10/2015
80593^131670-8262823Lelio R Paula04/2013
806019^49128-9062823Lelio R Paula05/2013
806111^60314-441062811Enzo Doria01/2013
8062(17*2^208614-1)/5362799Lelio R Paula01/2014
80632^208594+9362794Donovan Johnson06/2008
8064(-lucasV(1,2,417184)+2)/(3*104297)62788Mike Oakes02/2017
8065(2^208534+7)/905962772Lelio R Paula03/2012
8066(13^56333+1)/1462751Paul Bourdelais03/2010
806710^62750+5762751Robert Price01/2011
806810^62750-26742962750Patrick De Geest01/2013
80692^208427-6962743Lelio R Paula08/2011
80702^208421-11177562741Enzo Doria05/2014
80712^208404-11207962736Enzo Doria06/2014
80722^208343-222162718Yves Minet08/2013
80732^208335+51362716Lelio R Paula10/2011
8075(2^208328+47)/362713Lelio R Paula03/2012
807411^60220-204062713Enzo Doria12/2012
80762^208292+8162703Henri Lifchitz10/2005
807715013^15012-1501262698Henri Lifchitz10/2014
80782^208271-11274762696Enzo Doria06/2014
807911^60202-438062694Enzo Doria01/2013
8080(3^131403-4)/15762693Lelio R Paula04/2012
80812^208127-12666762653Paul Bourdelais01/2012
808271^33843+262653Lelio R Paula05/2013
8083(3^131325+7)/106685062652Lelio R Paula04/2012
80842^208019+11962620Lelio R Paula08/2011
8085(-lucasV(1,2,416078)+2)/(11*190717)62620Mike Oakes02/2017
808611^60126-1137062615Enzo Doria12/2012
80872^207976-248962608Yves Minet07/2014
8088(22699*2^207945+1)/28170962597Lelio R Paula06/2014
80894*21^47335+20562588Curtis Bright05/2015
809015^53210+862580Lelio R Paula05/2013
80912^207865+2962574Henri Lifchitz08/2005
809215^53199-3862567Lelio R Paula05/2013
8093(F(24947)^13-F(24946)^13)/F(24945)62560Wayne Halsdorf03/2012
80942^207782+5890562549Lelio R Paula10/2011
8095(2^207748-3)/843762535Lelio R Paula03/2012
8096(2^207711+5)/1362527Lelio R Paula03/2012
8097(268*10^62523-1)/362525Robert Price10/2017
809810^62523+6362524Robert Price01/2011
809910^62523-29237362523Patrick De Geest01/2013
81002^207691+1155*20769162522Henri Lifchitz02/2005
8101(lucasV(1,2,415410)+2)/(17*653)62522Mike Oakes02/2017
81022^207626-11215762502Enzo Doria06/2014
81033^130987+5262497Lelio R Paula04/2013
81048*6^80299-762486Lelio R Paula09/2014
810511^59997-267062481Enzo Doria12/2012
810693^31740+262480Lelio R Paula05/2013
8107(10^62451+119)/362451Serge Batalov12/2014
8108(2^207443+47)/764562443Lelio R Paula03/2012
81092^207364+11562423Lelio R Paula08/2011
81103^130815-4662415Lelio R Paula04/2013
8111(F(182)^1657-F(181)^1657)/F(180)62409Wayne Halsdorf03/2012
811220^47968-948362408Enzo Doria03/2013
8113(10^62402+101)/362402Robert Price04/2016
8114(13*2^207264-1)/362394Lelio R Paula01/2014
8115(79*10^62387-61)/962388Robert Price10/2015
81165^89244+3*2^8924462379Mike Oakes02/2010
81176^80160-1362377Lelio R Paula04/2013
8118(7*10^62362+53)/362363Robert Price10/2017
8119(1000121^10391+1)/100012262341Faysal YAtim07/2008
8120(17*10^62328-11)/362329Robert Price07/2015
81212^207023+1171562321Lelio R Paula09/2011
8122(265*10^62298+11)/362300Robert Price03/2017
81232^206947-6962298Lelio R Paula08/2011
81242^206938+2983562295Lelio R Paula02/2013
81252^206911-72687762287Paul Bourdelais03/2013
8126(6883*2^206884-1)/362282Lelio R Paula04/2015
81272^206892-11281762281Enzo Doria06/2014
8128(7*10^62278+113)/362279Robert Price10/2017
81293^130523+4662276Lelio R Paula04/2013
81302^206872-11345362275Enzo Doria07/2014
81312^206840-9362266Lelio R Paula08/2011
8132(1017*2^206815-1)/63562258Lelio R Paula04/2015
813396^31406+9562256Norbert Schneider03/2016
8134(2^206824+7)/64621362255Lelio R Paula03/2012
81352^206765-94168362243Paul Bourdelais11/2012
8136(6^79987-1)/562242Paul Bourdelais11/2007
81372^206755-157962240Yves Minet03/2013
813811^59764-582062238Enzo Doria01/2013
81395*10^62233+362234Dmitry Domanov11/2010
81408*3^130421+762228Lelio R Paula04/2014
814119^48661+1062226Lelio R Paula05/2013
8143(17*2^206705+1)/562225Lelio R Paula08/2012
81422^206705-11263562225Enzo Doria06/2014
81443^130403+868062219Lelio R Paula04/2013
814511^59740-711062213Enzo Doria01/2013
81472^206596-16762192Lelio R Paula08/2011
81462^206597+1891562192Lelio R Paula02/2013
81486^79918+13762189Lelio R Paula04/2013
8149lucasU(2408,1,18390)-lucasU(2408,1,18389)62186Mike Oakes05/2009
81502^206574+61362185Jason Earls04/2008
81513^130328+8062183Lelio R Paula04/2013
8152(lucasV(1,2,413270)-2)/(11^2*23*443*1871*2003*37571*687961)62181Mike Oakes02/2017
81532^206550+7681962178Enzo Doria05/2016
815411^59703-2462175Lelio R Paula05/2013
81552^206524+7578162170Enzo Doria04/2016
81562^206506+42762165Henri Lifchitz01/2005
81572^206465+769562153Lelio R Paula02/2013
81582^206464-164962152Yves Minet03/2013
81595^88917+5662151Lelio R Paula04/2013
81602^206444-11156962146Enzo Doria05/2014
81615^88908-4262145Lelio R Paula04/2013
816218^49495-2962130Lelio R Paula05/2013
81633*6^79842-562130Lelio R Paula09/2014
81647*10^62127-1762128Robert Price01/2017
81652^206373+841562125Lelio R Paula02/2013
816620^47745-958362118Enzo Doria03/2013
816741^38516-262118Lelio R Paula08/2013
81682^206332-5869562113Lelio R Paula09/2011
816911^59639-126062108Enzo Doria11/2012
81702^206232-1589362083Enzo Doria04/2013
8171(115*10^62073-1)/362075Serge Batalov12/2014
81722^206206+7579962075Enzo Doria04/2016
8173(74*10^62072+43)/962073Robert Price10/2015
81742^206194-18562071Lelio R Paula08/2011
81756^79757-10362064Lelio R Paula04/2013
8176p(13285)#/2-6462063Robert Price04/2017
8177(29*10^62030-41)/362031Robert Price07/2016
817820^47675-8162027Lelio R Paula06/2013
81793^129972+9862013Lelio R Paula04/2013
81802^205962+362001Donovan Johnson02/2006
81812^205933-205933^261993Henri Lifchitz05/2005
8182(68*10^61991+7)/361993Robert Price03/2016
818320^47641-66361983Enzo Doria03/2013
81843^129861+266061960Lelio R Paula04/2013
8185(55459*2^205800+1)/134561954Lelio R Paula06/2014
818618^49354-9761953Lelio R Paula05/2013
8187(209*10^61947-17)/361949Robert Price05/2017
818914*10^61937+108961939Jens K. Andersen11/2007
8188(11*2^205758-1)/5361939Lelio R Paula01/2014
819020^47600+6361930Lelio R Paula06/2013
8191(16384!+1185)/(3*5*79*10705361)61926Makoto Morimoto09/2017
819244117!3+24361918Robert Price09/2014
8193(31*2^205677-1)/5961915Lelio R Paula01/2014
8194(lucasV(1,2,411332)-2)/(13*97*137*929*40507)61900Mike Oakes02/2017
819520^47575-8161897Lelio R Paula06/2013
8196(58695*2^205593-1)/72761892Lelio R Paula04/2015
819787^31909+8661889Norbert Schneider10/2015
81982^205568+14161883Lelio R Paula08/2011
819910^61868+5892761869Patrick De Geest12/2012
820010^61868-3961868Robert Price05/2011
82015^88505-8861863Lelio R Paula04/2013
8202(-lucasV(1,2,411034)-2)/1463961863Mike Oakes02/2017
820413^55528-9861856Lelio R Paula05/2013
8203(55^35543-1)/5461856Paul Bourdelais08/2017
820530535!2-861844Robert Price06/2015
820611^59371-120061829Enzo Doria11/2012
82077*2^205370-561824Lelio R Paula04/2014
8208(47*10^61821+403)/961822Robert Price04/2017
82092^205275+769561794Lelio R Paula02/2013
82102^205269+1291561793Lelio R Paula02/2013
8211(47*2^205265+1)/3561792Lelio R Paula04/2015
821219^48309+4061776Lelio R Paula05/2013
8213(424*10^61770-1)/961772Robert Price11/2017
82142^205192-407961769Yves Minet06/2011
82152^205184+1609561767Lelio R Paula09/2011
821620^47472-342361763Enzo Doria03/2013
8217(17*10^61760-89)/961761Robert Price11/2017
82182^205149-179561757Lelio R Paula09/2011
82192^205110-1761745Lelio R Paula08/2011
8220(373^24007+1)/37461737Eric Chen10/2017
8221(2^205025-7)/2561718Lelio R Paula03/2012
822227^43117-26^4311761717Robert Price08/2012
82232^205016+3761716Lelio R Paula08/2011
8224gcd(V(738275),5*F(147655)*(F(147655)-1)+1)61715Serge Batalov04/2015
82251263^19898+19898^126361712Serge Batalov05/2014
8226135^28963-13461701Norbert Schneider04/2015
8227(33*2^204966+1)/23434161698Michael Porter01/2015
8228(7*10^61696+167)/361696Robert Kinser10/2017
8229(46*10^61693+17)/961694Robert Price06/2015
8230((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+6676861684Phil Carmody09/2004
82311850^18879+18879^185061681Serge Batalov05/2014
82332^204891-100561679Lelio R Paula09/2011
8232151^28306-261679Lelio R Paula10/2017
8234(3^129271-5)/4150661674Lelio R Paula03/2012
823515937^7408+7408^1593761672Hans Havermann02/2017
82365^88216-1261661Lelio R Paula04/2013
823718185^2454+2454^1818561645Hans Havermann01/2017
82392^204767-1586561642Enzo Doria04/2013
8238(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
82407*2^204751-961638Lelio R Paula04/2014
82424*10^61625+2161626Robert Price08/2016
824115369^10226+10226^1536961626Hans Havermann02/2017
82432^204702-1812561622Enzo Doria05/2013
82445*3^129146+861620Lelio R Paula04/2014
82452^204673+12961613Lelio R Paula08/2011
824618^49079+9761608Lelio R Paula05/2013
8247106^30416+10561602Norbert Schneider12/2016
82482^204590-3361588Lelio R Paula08/2011
82492^204586-11197561587Enzo Doria06/2014
82502^204580-1607761585Enzo Doria04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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